The effect of perturbations of operator-valued frame sequences and fusion frames on their duals

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answ...

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Autores principales:	Kutyniok, G., Paternostro, V., Philipp, F.
Formato:	JOUR
Materias:	Dual frame Frame sequence Fusion frame Fusion frame dual Operator-valued frame Perturbation
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_18463886_v11_n2_p301_Kutyniok
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_18463886_v11_n2_p301_Kutyniok
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spelling	todo:paper_18463886_v11_n2_p301_Kutyniok2023-10-03T16:33:11Z The effect of perturbations of operator-valued frame sequences and fusion frames on their duals Kutyniok, G. Paternostro, V. Philipp, F. Dual frame Frame sequence Fusion frame Fusion frame dual Operator-valued frame Perturbation Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answered. In this paper, we quantitatively measure this stability by considering the associated deviations of the canonical and alternate dual sequences from the original ones. It is proven that operator-valued frame sequences are indeed stable in this sense. Along the way, we also generalize existing definitions for fusion frame duals to the infinite-dimensional situation and analyze how they perform with respect to a list of desiderata which, to our minds, a fusion frame dual should satisfy. Finally, we prove a similar stability result as above for fusion frames and their canonical duals. © ELEMEN, Zagreb. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_18463886_v11_n2_p301_Kutyniok
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Dual frame Frame sequence Fusion frame Fusion frame dual Operator-valued frame Perturbation
spellingShingle	Dual frame Frame sequence Fusion frame Fusion frame dual Operator-valued frame Perturbation Kutyniok, G. Paternostro, V. Philipp, F. The effect of perturbations of operator-valued frame sequences and fusion frames on their duals
topic_facet	Dual frame Frame sequence Fusion frame Fusion frame dual Operator-valued frame Perturbation
description	Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answered. In this paper, we quantitatively measure this stability by considering the associated deviations of the canonical and alternate dual sequences from the original ones. It is proven that operator-valued frame sequences are indeed stable in this sense. Along the way, we also generalize existing definitions for fusion frame duals to the infinite-dimensional situation and analyze how they perform with respect to a list of desiderata which, to our minds, a fusion frame dual should satisfy. Finally, we prove a similar stability result as above for fusion frames and their canonical duals. © ELEMEN, Zagreb.
format	JOUR
author	Kutyniok, G. Paternostro, V. Philipp, F.
author_facet	Kutyniok, G. Paternostro, V. Philipp, F.
author_sort	Kutyniok, G.
title	The effect of perturbations of operator-valued frame sequences and fusion frames on their duals
title_short	The effect of perturbations of operator-valued frame sequences and fusion frames on their duals
title_full	The effect of perturbations of operator-valued frame sequences and fusion frames on their duals
title_fullStr	The effect of perturbations of operator-valued frame sequences and fusion frames on their duals
title_full_unstemmed	The effect of perturbations of operator-valued frame sequences and fusion frames on their duals
title_sort	effect of perturbations of operator-valued frame sequences and fusion frames on their duals
url	http://hdl.handle.net/20.500.12110/paper_18463886_v11_n2_p301_Kutyniok
work_keys_str_mv	AT kutyniokg theeffectofperturbationsofoperatorvaluedframesequencesandfusionframesontheirduals AT paternostrov theeffectofperturbationsofoperatorvaluedframesequencesandfusionframesontheirduals AT philippf theeffectofperturbationsofoperatorvaluedframesequencesandfusionframesontheirduals AT kutyniokg effectofperturbationsofoperatorvaluedframesequencesandfusionframesontheirduals AT paternostrov effectofperturbationsofoperatorvaluedframesequencesandfusionframesontheirduals AT philippf effectofperturbationsofoperatorvaluedframesequencesandfusionframesontheirduals
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The effect of perturbations of operator-valued frame sequences and fusion frames on their duals

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